1) What is numerically interesting about April 25, 1849 - the date of birth of the German mathematician Felix Klein - and why is this year’s anniversary particularly noteworthy?

Solution His birthday is 25/4/1849, which is 22/52/432, and he is celebrating his 169th = 132 anniversary. All the numbers are squares. Extra marks if you spotted they are all primes. Klein was destined to be a mathematician!

2) What happens when you draw two parallel lines down a Möbius strip as below and then cut along them?

(If you are reading this for the first time, check out the story where I explain in more detail what a Möbius strip is and why it is interesting.)

Here’s how you might have thought this through. Cutting along the lines is like trimming the sides of a central band. This central band retains the form of a Möbius strip, just a thinner one.

The trimmed edges are both joined, and they become the longer loop with two twists. Remember, in the set up I told you that when you draw a single line down a Möbius strip and cut along it you get a single loop with two twists. In the case with two lines, imagine the two lines becoming closer and closer together. In the limit they are the single line.

If you want more fun with Möbius strips, first make two more bands. Mark a line down the middle of each of them, and stick them together as below: